Numerical differentiation of implicitly defined curves

Muhammed I. Syam; Hani I. Siyyam

doi:10.1016/S0377-0427(99)00106-5

Numerical differentiation of implicitly defined curves

Muhammed I. Syam, Hani I. Siyyam

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

Abstract

In this paper we develop a finite differencing device to calculate approximations of derivatives c′(0),c″(0),... of regular solution curves c:R∋s→c(s)∈Rⁿ of nonlinear systems of equations f(x)=0,f∈C^k(Rⁿ⁺¹,Rⁿ) without having to compute points on the solution curve c(s). The derivative vectors c′(0),c″(0),... can be used in the numerical approximation of the solution set f^-1(0) to construct higher-order predictors to be used in the predictor-corrector continuation method.

Original language	English
Pages (from-to)	131-144
Number of pages	14
Journal	Journal of Computational and Applied Mathematics
Volume	108
Issue number	1-2
DOIs	https://doi.org/10.1016/S0377-0427(99)00106-5
Publication status	Published - Aug 15 1999

Keywords

Continuation method
Implicitly defined curve* Higher order predictor
Numerical differentiation

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/S0377-0427(99)00106-5

Cite this

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title = "Numerical differentiation of implicitly defined curves",

abstract = "In this paper we develop a finite differencing device to calculate approximations of derivatives c′(0),c″(0),... of regular solution curves c:R∋s→c(s)∈Rn of nonlinear systems of equations f(x)=0,f∈Ck(Rn+1,Rn) without having to compute points on the solution curve c(s). The derivative vectors c′(0),c″(0),... can be used in the numerical approximation of the solution set f-1(0) to construct higher-order predictors to be used in the predictor-corrector continuation method.",

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AU - Syam, Muhammed I.

AU - Siyyam, Hani I.

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AB - In this paper we develop a finite differencing device to calculate approximations of derivatives c′(0),c″(0),... of regular solution curves c:R∋s→c(s)∈Rn of nonlinear systems of equations f(x)=0,f∈Ck(Rn+1,Rn) without having to compute points on the solution curve c(s). The derivative vectors c′(0),c″(0),... can be used in the numerical approximation of the solution set f-1(0) to construct higher-order predictors to be used in the predictor-corrector continuation method.

KW - Continuation method

KW - Implicitly defined curve Higher order predictor

KW - Numerical differentiation

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EP - 144

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1-2

ER -

Numerical differentiation of implicitly defined curves

Abstract

Keywords

ASJC Scopus subject areas

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